Complex Spatially-Resolved Reflectometry/Refractometry

ABSTRACT

Apparatus and methods for complex imaging reflectometry and refractometry using at least partially coherent light ( 121 ). Quantitative images yield spatially-dependent, local material information about a sample ( 128, 228 ) of interest. These images may provide material properties such as chemical composition, the thickness of chemical layers, dopant concentrations, mixing between layers of a sample, reactions at interfaces, etc. An incident beam ( 123 ) of VUV wavelength or shorter is scattered off of a sample ( 128, 228 ) and imaged at various angles, wavelengths, and/or polarizations. The power of beam ( 123 ) is also measured. This data is used to obtain images of a sample&#39;s absolute, spatially varying, complex reflectance or transmittance, which is then used to determine spatially-resolved, depth-dependent sample material properties.

This invention was made with government support under grant numberDMR1420620 awarded by the National Science Foundation. The governmenthas certain rights in the invention.

FIELD OF THE INVENTION

The field of the present invention is high-resolution, quantitativeimaging that can elucidate the depth-dependent composition of samples.In particular, high resolution and high composition sensitivity areachieved by using sub-VUV wavelengths to perform complex imagingreflectometry or refractometry.

BACKGROUND OF THE INVENTION

Prior art in the field (US20160187849A1) has described how to performcoherent diffraction imaging with arbitrary angle of incidence, at highnumerical aperture, allowing for high resolution images to be collectedin transmission or reflection at any incidence angle of the illuminatingbeam.

Prior art in the field has described imaging reflectometers. U.S. Pat.No. 7,067,818 B2 describes an imaging reflectometer at sub-VUVwavelengths that uses a spectrometer to obtain properties similar tothose described here. The technique described in this patent does notrequire the use of a spectrometer, however, making it more general andmore easily applied. The current patent represents the first compleximaging reflectometer to our knowledge, where both an amplitude andphase image of an object are obtained.

Prior art in the field (for example, Nature Communications 4, (2013),pp. 1669-1675 and Optics Express 24, (2016), pp. 18745-18754) has usedmultiple wavelengths to determine spatially-dependent materialproperties of samples. In works such as these, the absolute reflectanceor transmittance of the sample is not measured (that is to say, onlyrelative reflectivities or transmissivities are measured). Further,there is no determination of the depth-dependent material properties ofthe sample. Finally, such works typically rely upon using wavelengthsthat fall at an absorption edge of the sample, which the method andapparatus presented here do not. Thus, this patent is more broadlyapplicable to determining the material properties of a wider variety ofsamples.

Quantitative imaging techniques are those that extractspatially-dependent material properties of samples, typically usingwell-understood, specific contrast mechanisms that depend on materialproperties of interest. Such techniques typically elucidate thecomposition of a sample in addition to its morphology, and are capableof separating these measurements.

Reflectometry is the use of reflected waves from surfaces tocharacterize objects. Refractometry is the use of transmitted wavesthrough an object to characterize it. If such a technique results inmeasurements of an object's spatially-resolved characteristics, then itis called imaging reflectometry or refractometry. Furthermore, if theseimages are complex-valued (that is, if an object's amplitude and phaseare measured), then the technique is referred to as complex imagingreflectometry or refractometry. In this patent, “scattered light” isdefined as light that has interacted with a sample. This includesdiffracted and refracted light collected in either a transmission orreflection geometry.

In this patent, “complex reflectance” or “complex transmittance” refersto complex-values that may be decomposed as r=R exp(i φ_(t)) or t=Texp(i φ_(t)). The absolute value of the reflectance, R, is called thereflectivity. Similarly, the absolute value of the transmittance, T, iscalled the transmissivity. Both reflectivity and transmissivity take ona value between 0 and 100%, and describe the percent of the incidentpower that would be measured on a detector after a beam is reflectedfrom or transmitted through a sample. The phase, φ_(r) or φ_(t) is thephase shift that a reflected or refracted wave from the sample wouldhave with respect to the incoming beam. In this patent, the term complexscattering properties refers to either the complex reflectance orcomplex transmittance or, in some cases, both.

Coherent diffractive imaging (CDI) is a microscopy technique that may beperformed either in transmission or reflection geometries. In eithercase, a loosely focused, partially to fully coherent beam illuminates asample and scattered light is recorded on an array detector (camera),with no lens or other optic required in between the sample and thecamera. The camera records one or many scatter patterns related in aknown way to the light leaving the sample. A computer algorithm, or“phase retrieval algorithm”, may be used to retrieve the amplitude andphase of the light leaving the sample from these scatter patterns. Insingle diffraction pattern CDI, one diffraction pattern is recorded atone sample position. In ptychography CDI, the sample is area-by-areatranslated with overlap between scan positions. Multiple diffractionpatterns are recorded with redundant information existing in thedataset. This redundant dataset allows for robust reconstruction of boththe sample and the illumination separately, with a complex image beingretrieved for each.

Short wavelength illumination (vacuum ultraviolet through soft x-ray) isuseful for producing high resolution images within the diffraction limitof light. In recent years, it has been paired successfully with lenslessimaging techniques such as coherent diffraction imaging, scanning pointmicroscopy and holography to yield amplitude and phase contrast imagesof samples with ultrahigh resolution. In particular, extreme ultravioletlight (with a wavelength of 10-100 nm) has proved useful because imagesobtained using these wavelengths show significant amplitude and phasecontrast for many samples, due to a multiplicity of absorption edgesfalling in this spectral region. In this patent, “beam” or“illumination” is used to mean light, electrons, neutrons, or otherradiation that will scatter from a sample.

Holography is an alternative method for obtaining complex images ofsamples in which a reference wave is interfered with light scatteringfrom a sample. For the purposes of this patent, “phase retrieval” shallinclude holographic techniques capable of separating the sample from theillumination. Furthermore, complex images of a sample's reflectance ortransmittance could instead be acquired by performing interferometric,point-by-point scanning microscopy in a transmission (STXM) orreflection (SRXM) geometry. In such an interferometric STXM/SRXMmeasurement, the scattered beam would be interfered with a knownreference. Thus, the scatter data discussed in this patent may consistof holographic datasets, coherent diffraction imaging datasets, orinterferometric scanning point microscopy measurements. The preferredembodiment will focus on the use of ptychographic coherent diffractionimaging data, but an expert in the field will understand that anyimaging technique that can yield complex reflectance or transmittanceimages are alternative embodiments of this patent.

SUMMARY

It is an object of the present invention to provide complex,spatially-resolved reflectometry and refractometry via quantitativemicroscopy techniques using at least partially coherent light.Quantitative images yield spatially-dependent, local materialinformation about a sample of interest. These images may providematerial properties such as chemical composition, the thickness ofchemical layers, dopant concentrations, mixing between layers of asample, reactions at interfaces, etc. Preferred embodiments relate tocoherent diffraction imaging, holography, or interferometric scanningpoint microscopy as applied using short-wavelength deep-ultraviolet(DUV), vacuum ultraviolet (VUV), extreme ultraviolet (EUV), or softx-ray light sources. These techniques are used to obtain images of asample's absolute, spatially varying, complex reflectance ortransmittance, which may be used to determine spatially-resolved,depth-dependent sample material properties.

Most coherent diffraction imaging to date has not been quantitative.Intensity images of reconstructed objects have yielded relativereflectivity or transmissivity values between different pixels, but withno absolute normalization. The present invention provides a method toobtain absolute, complex reflectance or transmittance images fromcoherent diffraction imaging—which could alternatively be replaced withvarious holographic or interferometric scanning-point microscopytechniques—and use these images to determine material properties of asample. Scatter data from an illumination source interacting with asample is recorded on a detector in either a reflection or transmissiongeometry. Then, any phase retrieval algorithm or other interferometricmethod that can separate the illumination from the object to yieldcomplex reflectance or transmittance images of the sample may be used.When using coherent diffraction imaging, if the reconstructedillumination is normalized to a measurement of the illumination's power,then absolute reflectance or transmittance images may naturally beobtained.

Furthermore, multiple complex images of the sample are collected, eachwith a varying “independent parameter”. This independent parameter couldbe the beam's incidence angle (the focus of the preferred embodiment),polarization, or wavelength. The resulting complexreflectance/transmittance vs. independent parameter(angle/wavelength/polarization) curves for each pixel in the image, orfor groups of pixels known to share very similar composition, may thenbe used to determine spatially-resolved, depth dependent materialproperties for multiple regions of the sample.

These properties include chemical composition, density, interfacialmixing, dopant concentrations, surface roughness and layer thicknesses.The use of both the reflectivity or transmissivity and phase of a samplefor determining material properties makes this a powerful technique thathas significantly more sensitivity than the use of the amplitude alonein traditional imaging reflectometry.

A preferred method according to the present invention determinesspatially-resolved, material properties from a sample's complexreflectance or transmittance by providing at least partiallyspatially-coherent radiation in the form of an incident beam,characterizing the incident beam (for example by measuring its power),delivering the incident beam onto a sample to produce scatteredradiation, varying at least one independent parameter of the incidentbeam upon which the sample's complex reflectance or transmittance isdependent, collecting the scattered radiation at multiple values of theindependent parameter on a detector and generating scatter data,calculating spatially-resolved, complex scattering properties of thesample based upon the beam characterization and the scatter data anddetermining spatially-resolved, depth-dependent material properties ofthe sample from the spatially-resolved complex scattering properties. Aniterative method of determining the depth-dependent properties isespecially useful. In this case, the method includes the step ofguessing at least one sample model in which spatially-resolved materialproperties are assigned a depth (e.g. dopant density, material density,material composition, surface roughness, or interfacial mixing ofinterfaces between layers). Then, the method estimates predictedreflectance/transmittance versus the independent parameter based on thesample model, compares the predicted reflectance/transmittance versusthe independent parameter to a measurement of reflectance/transmittanceversus the independent parameter, and refines the sample model until thepredicted reflectance/transmittance versus the independent parametersubstantially agrees with the measured reflectance/transmittance versusthe independent parameter. A genetic algorithm is useful here.

The method may use either the amplitude or phase of the complexscattering properties to determine material properties. Vacuumultraviolet (VUV) or shorter wavelength light may be used for theincident beam, for example by generating the light via high harmonicgeneration.

The incident beam may provide multiple illuminating wavelengthssimultaneously incident on the sample, provide multiple illuminatingwavelengths in sequence incident on the sample, provide multiplepolarization states of the incident beam, or provide multiple spatialmodes of the incident beam. Then the independent parameter might beillumination wavelength, relative incidence angle between the beam andthe sample, or illumination polarization.

In some cases it is useful to move the sample relative to the incidentbeam and collect the scattered radiation for multiple values of theindependent parameter. The camera may be moved with respect to thescattered radiation to extend the resolution of the imaging systembetween variations of the independent parameter.

If the beam is characterized by measuring beam power, this may be donerepeatedly during the process, either by removing the sample from thepath of the beam or by scattering the beam off of a portion of thesample having known properties.

This method may use a ptychographic reconstruction algorithm.

Apparatus according to the present invention for measuringspatially-resolved material properties of a sample includes an opticthat focuses an incident beam of light composed of wavelengths at orbelow the vacuum ultraviolet onto the sample, a detector configured tocollect light that scatters from the sample and generate scatter data, adevice configured to measure power of the incident beam, and a processorconfigured to convert scatter data and measured power of the incidentbeam into spatially-resolved, complex scattering properties of thesample, and determine spatially-resolved material properties of thesample from the spatially-resolved complex scattering properties. It mayinclude an optic to divert a portion of the beam to the detector, amechanism configured to rotate the sample relative to the incident beam,a mechanism configured to translate the sample relative to the incidentbeam, a mechanism configured to rotate the detector relative to thesample a mechanism for selectively removing the sample from a path ofthe beam between the optic and the array detector, or a mechanism toalter the wavelength of the illumination on the sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C are schematic, top-down views of a complex imagingreflectometer in various configurations according to the presentinvention. FIG. 1A shows a configuration that would be suitable for anindependent parameter that is the beam wavelength or polarization. FIG.1B shows a configuration of a reflectometer where the independentparameter is beam incidence angle. FIG. 1C shows a suitableconfiguration of the reflectometer for obtaining beam data.

FIGS. 2A-C are schematic, top-down views of a complex imagingrefractometer in various configurations according to the presentinvention. FIG. 2A shows a configuration that would be suitable for anindependent parameter that is the beam wavelength or polarization. FIG.2B shows a configuration of a refractometer where the independentparameter is beam incidence angle. FIG. 2C shows a suitableconfiguration of the refractometer for obtaining beam data.

FIG. 3 is a flow diagram illustrating the process of obtaining complexreflectance or transmittance vs. incidence angle (or other independentparameter) curves from spatially resolved areas of a sample, using datacollected via complex imaging reflectometry or refractometry as shown inFIGS. 1A-C and FIGS. 2A-C.

FIG. 4 is a flow diagram illustrating the process of obtaining spatiallyresolved sample composition information from the complex reflectivity ortransmissivity measurements obtained as shown in FIG. 3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

This patent is concerned with a work flow that includes the collectionof scattered radiation measurements from a sample, the use of thesemeasurements to determine the complex, spatially-resolved, absolutereflectance or transmittance of the sample in an area of interest, forthe ultimate deduction of spatially-resolved material properties of thesample.

The preferred embodiment of this invention is an instrument thatmeasures a spatially-resolved image where each pixel yields the complex,absolute reflectance or transmittance (including both amplitude andphase) of a sample from a dataset consisting of scatter data due to asub-VUV wavelength illumination beam incident on a sample.

The instrument collects diffraction data from an at least partiallyreflective sample 128 or at least partially transmissive sample 228 atfor a multiplicity of values of an independent parameter (multipleincidence angles, wavelengths, or polarizations). For each value of theindependent parameter(s) (310, 320, 330), scatter data from multipletranslations between the illumination and sample (311, 321, 331) may becollected. A complex-valued image 500 is reconstructed 400 for eachvalue of the independent parameter(s).

FIGS. 1A-1C are schematic, top-down views of a complex imagingreflectometer in various configurations according to the presentinvention. The independent parameter for which these schematics areshown is beam incidence angle. Note that the apparatus in FIGS. 1A-C andFIGS. 2A-C is the same for convenience, but not all of the elements willbe required in every embodiment. For example, the configurations of FIG.2A-C may not require the sample rotation stage 124 if the independentparameter is not beam incidence angle. Translation stages 125-127 may ormay not be used, but are consistent with a reflectometer wherein scatterpatterns for multiple relative translations between the beam and thesample are collected for each value of the independent parameter(s).

FIG. 1A shows a complex imaging reflectometer in a first data collectiongeometry for light incident on a sample at initial angle θm (133). Abeam of partially to fully coherent radiation 121 is incident onto afocusing optic 122 and focused as incident beam 123 onto a reflectivesample 128 at initial incident angle 133. Sample 128 sits atop Z (127)and Y (126) translation stages that allow the beam's focus to beincident at different relative translations on the sample's surface.Sample 128, Z stage 127, and Y stage 128 sit atop X translation stage125 that allows the sample's face to be aligned with the axis ofrotation 129 of sample rotation stage 124 below. Scattered light 130from sample 128 forms scatter data 300 (see FIG. 3) collected via camera131 which sits atop camera rotation stage 132, which rotates camera 131about axis of rotation 129. Sample stage 124 is rotated in order torecord scatter data on camera 131 at a multiplicity of incidence anglesof beam 123, as shown in FIG. 1B.

FIG. 1B shows a complex spatially-resolved reflectometer configured forcollection of scattered light at a variable incidence angle θ_(n) (144).Sample 128 is rotated by angle de (144). Camera 131 is rotated aboutaxis of rotation 129 by an angle 2 dθ (145) such that the specularreflection 130 from the sample remains centered on camera 131. Thus,θ_(n)=θ_(m)+dθ.

Scatter data from multiple translations using Y stage 126 and Z stage127 may be recorded at each value of the independent parameter (here,incidence angles 144). Not shown, a rotation stage with axis of rotationbeing the X axis could be added between Z stage 127 and sample 128, orin lieu of the Z and Y stages such that multiple relative rotationsbetween the sample and the beam could replace or add to the multipletranslations recorded at every value of the independent parameter.Scatter data is collected for many values of the independent parameter(incidence angles 144, in FIG. 1B) in this manner.

FIG. 1C shows a configuration for collecting incident beam 123 data, inparticular beam power and optionally shape on the detector. Eitherbefore, after, or before and after scatter data 130 has been collectedat many incidence angles 144 and possibly sample translations, beam datais acquired as shown in FIG. 1C. Sample 128 is rotated as shown byarrows 170 such that its face is parallel to incoming beam 123. Sample128 is then translated using X translation stage 125 such that it doesnot intersect focusing beam 163 or defocusing beam 169. Camera 131 isrotated using rotation stage 132 such that its face is perpendicular todefocusing beam 169. One or more images of the beam are acquired in thisgeometry. Beam data may be collected between collecting images ofscattered light 130 at varying angles 144. Alternatively, the beam maybe sampled and monitored simultaneously during scatter data acquisition(for example using a beamsplitter and photodiode or second camera placedbefore 121, not shown). Beam images are summed after backgroundsubtraction to yield the power of the beam. The beam shape recorded inthe beam images may also be used to improve the reconstruction quality,as described in the Modulus Enforced Probe patent.

FIGS. 2A-C are schematic, top-down views of a complex imagingrefractometer in various configurations according to the presentinvention.

The data collection methodology is similar to the case of thereflectometer shown in FIGS. 1A-C. In this case, sample 228 is partiallytransmissive to the radiation of incident beam 123. Camera 131 is placedperpendicular to the incident focusing beam 133.

In the reflection geometry of FIGS. 1A-C, sample 128 is mounted on arotation stage 124 whose axis of rotation is the Z axis. The camera ismounted on a separate out-of-plane camera rotation stage 131 whose axisof rotation 129 is closely aligned to that of sample rotation stage 124.For the embodiment in which the independent parameter is incidenceangle, the rotation stages 124, 132 are used to collect scatter patternsat a variety of incidence angles 133, 143 of the illumination, with (inthe embodiment of FIG. 1B) camera 131 moving through twice the angle 145of the sample at each imaging position such that the specular reflectionfrom the sample is always pointed at the center of the camera.

In the transmission geometry of FIGS. 2A-C, sample 228 is still rotatedto collect data at various incident angles 143, but camera 131 mayremain stationary because the undiffracted, transmitted beam 230 is notdeflected. At each incidence angle 143, either one diffraction patternmay be collected or the sample may be area-by-area scanned in-plane(using Y translation stage 126 and Z translation stage 127) with overlapbetween positions, resulting in a dataset for each incidence angle 143that may be reconstructed using ptychographic coherent diffractionimaging.

FIG. 2A is the transmissive analogous configuration to the configurationof FIG. 1A. Again, input beam 121 is focused by optic 122, resulting inincident beam 123 at initial incident angle 133. Scattered light 230 isincident on camera 131, which collects scatter data 300 (see FIG. 3). InFIG. 2B, incident angle 143 is varied increments de and scatter data iscollected. In FIG. 2C, sample 228 is removed from the path between optic122 and camera 131, and unscattered beam data 169 is gathered directly.

For a sample that is both partially reflecting and partiallytransmitting, collecting scatter data in both transmission andreflection geometries can be useful, and the reconstruction of bothcomplex reflectance and transmittance images can be useful. A way tocollect both is by rotating camera 131 from the reflected side of thesample to the transmitted side between variations of the independentparameter.

The sub-VUV wavelength light 121 described above may be generated viahigh harmonic generation, or on a facility-scale source by a synchrotronor x-ray free electron laser. If a high harmonic source is used, onenarrow-band harmonic may be selected using wavelength-selecting mirrorsto illuminate the sample, in which case a reconstruction algorithm suchas the extended ptychographic iterative engine (ePIE) may be used toperform phase retrieval. Alternatively, multiple harmonics may be used,illuminating the sample one at a time or all at once, in which case areconstruction algorithm such as ptychographic information multiplexing(PIM) may be used to perform phase retrieval.

Regardless of the reconstruction algorithm, if coherent diffractionimaging (as opposed to holography or interferometric scanning pointmicroscopy) is used, the power in the solved-for illumination at eachwavelength should be constrained to be equal to the power in the beamincident on the sample. This may be achieved, for example, by summingthe detector counts in an image of the beam obtained by reflecting thebeam off a smooth mirror of known reflectivity, or by moving 270 thesample out of the way and moving detector 131 into the undiffractedbeam, or by using the Modulus-Enforced Probe technique (shown anddescribed in the patent application entitled “Modulus-Enforced Probe”filed concurrently with this application and having inventors MichaelTanksalvala, Daniel Adams, Dennis Gardner, Christina Porter and GiuliaMancini, and incorporated herein by reference). Alternatively, theincident beam's power may be measured by a calibrated photodiode. Thedetected scatter patterns must then be converted to the same units asthe diode measurement using knowledge of the detector's quantumefficiency and the wavelength of the illumination.

If such normalization is performed properly, each reconstructed sampleintensity image will naturally be equal to the reflectivity ortransmissivity of the sample. This technique is called reconstructedabsolute phase-diverse transmissivity or reflectivity CDI, or RAPTR CDI,and is described, for example, in Nano Letters 2016, 16 (9), pp5444-5450. Furthermore, a beamsplitter and photodiode or second cameramay be used to sample and monitor the power of the illuminationsimultaneously during data acquisition. This beamsplitter may be placedeither before or after the focusing optic. There may be a diffractiongrating placed in between the beamsplitter and the second camera todetermine and monitor the spectral weights of wavelengths in theillumination if multiple wavelengths are being used. These measurementsmay be easily converted to detector counts so long as one undiffractedbeam image is also collected on the detector measuring the scatterpatterns (as shown in FIG. 1C, for reflection and FIG. 2C fortransmission). The beam normalization described above may then becarried out on a per-position basis in the phase retrieval algorithmsdescribed previously. Monitoring the beam in this manner significantlydecreases the sensitivity of the system to fluctuations in the incidentbeam's power.

In order to extend the spatial resolution (that is, the numericalaperture) of a spatially-resolved reflectometer or refractometer of thepresent invention, with the sample 128 or 228 held fixed, the camera 131may be rotated such that the specular reflection (or the non-deflectedtransmitted beam) no longer points at the center of camera 131. Bycollecting diffraction patterns at a variety of camera rotations usingrotation stage 124 (typically moving the camera through a small enoughrotation at each step that there is overlap in the collected diffractionpattern with the previous step), high spatial frequency diffraction datais collected. These diffraction patterns may then be combined to producea single, high-resolution diffraction pattern that extends towavelength-limited spatial frequencies. The numerical aperture of thesystem may be extended in multiple dimensions if a third rotation stagethat rotates the sample in the YZ plane about the X axis (withcoordinates as shown in FIGS. 1A-2C) is used to rotate the samplein-plane. With the independent parameter held fixed, at each in-planesample rotation position, camera 131 is also rotated. Then, alldiffraction patterns from the various in-plane rotations and camerarotations may be stitched together to create a single, high numericalaperture diffraction pattern for a particular illumination incidenceangle and sample translation. This procedure would then be carried outfor each value of the independent parameter.

FIG. 3 is a flow diagram illustrating how scatter datasets (310, 320,330) for various values of the independent parameter (collected asdescribed above), may be used to obtain spatially resolved reflectanceor transmittance vs. independent parameter curves (700). Each scatterdataset may consist of one or many scatter patterns (311, 321, 331)which may result, for example, from many relative translations orin-plane rotations of the sample.

The scatter datasets are reconstructed in step 400 using phase retrievalwhere the beam power is enforced using the beam data (302). This mayinclude using ptychography, single diffraction pattern CDI, orholographic reconstruction techniques. In reconstruction step 400, beamdata 302 is used as a normalization, ensuring that the reflectivity ortransmissivity in the output images is an absolute measurement taking ona value between 0 and 1. Beam data 302 is collected, for example, asshown in FIG. 1C and FIG. 2C.

Reconstruction step 400 results in a complex image (510, 520, 530) foreach of the values of the independent parameter. These complex imagesare represented as absolute reflectivity or transmissivity images (501)and phase images (502). In step 600, reflectance from individual pixelsor groups of pixels corresponding to the same spatial location in eachcomplex image (510, 520, 530) is plotted as a function of theindependent parameter. The output of this step is shown in FIG. 700, andwill hereafter be referred to as the measurement.

Spatial averaging may optionally be performed for pixels within regionsof each image that have similar reflectances/transmittances. Forexample, in FIG. 3, all pixels in images 500 are divided into twocategories: structures (540) and substrate (550).

Correspondingly, only reflectance/transmittance curves for the spatiallyaveraged values of the structures and substrate are extracted in 700.The number of groups of pixels for which the reflectance/transmittanceis measured (i.e. the amount of spatial averaging performed) may be muchlarger than two. In the limit, measurements 700 could consist ofseparate curves for every pixel in images 500. If a smaller amount ofspatial averaging is performed, the spatial resolution of the ultimatesample composition measurement higher. If more spatial averaging isperformed, the ultimate sample composition measurements will be morerobust to noise, in general.

FIG. 4 is a flow diagram showing how the spatially-resolvedreflectance/transmittance measurements in step 700 may be used to obtainthe spatially-resolved, depth-dependent composition of the sample. Forsimplicity, FIGS. 3 and 4 show reflectance and in turn compositiondetermined for only two categories of pixel in the reconstructed images(structures and substrate), but this determination of composition couldbe done for smaller groups of pixels or on a pixel-by-pixel basisinstead. Based on prior knowledge of the sample, a population of guesses800 for plausible composition vs. depth profiles of the sample aregenerated. Each guess consists of a separate composition vs. depthprofile for every pixel group identified in 700 (for example, structures540 and substrate 550).

In step 900, the interaction of the guessed sample compositions withsub-VUV wavelength light is modeled. This modeling may consist ofrepresenting each region of interest in the sample (i.e. structures 540and substrate 550) as a stack of thin layers with differing refractiveindex per layer. Then, reflectance or transmittance vs. independentparameter curves are generated, for example by solving Maxwell'sequations (or the Fresnel equations) in the stack. This is well doneusing a rigorous coupled-wave analysis (RCWA) computation. The result isa prediction of the sample's reflectance or transmittance 1000, forevery value of the independent parameter, for every sample guess inpopulation 800.

The predicted reflectance or transmittance curves are next compared instep 1100 to the measurement 700. An error metric such as the meansquared error is used to evaluate how close each prediction 1000 is tomeasurement 700. Next, a new population of possible samples is guessedin step 1200. The new guess population may be generated with a geneticalgorithm. Such an algorithm typically eliminates guesses from theprevious guess population 800 that produced predictions 1000 that werefar from measurement 700, while keeping and/or combining guesses thatyielded predictions 1000 close to measurement 700. Steps 800-1200 areiterated, refining the sample model until one of the sample guessescorresponds to a prediction 1000 for the reflectance/transmittance thatagrees sufficiently well (1300) with measurement 700. Sufficiently wellmeans, for example, that the error calculated in comparison 1100 fallsbelow some pre-set threshold. Once step 1300 returns “true” (i.e. onceagreement has been reached between the model and the measurement), theguessed sample composition that results in the lowest error betweenprediction 1000 and 700 is taken to be equal to the sample'scomposition. Once again, note that composition vs. depth profiles 1400may be extracted pixel-by-pixel or for regions of the sample (i.e.structures 540 and substrate 550) known to have nearly-identicalcomposition. Spatial averaging over many pixels of the image mayincrease composition sensitivity.

The result of the workflow of this patent is output 1400, a set ofdepth-dependent chemical concentrations for spatially-resolved regionsof a sample. Accordingly, the technique can characterize in aspatially-resolved manner a variety of relevant quantities. These mayinclude the sample's depth-dependent complex index of refraction, dopantconcentrations, layer thicknesses, density, surface roughness,interfacial mixing (i.e. diffusion) at interfaces between layers, ordynamically changing compositions over time (including, but not limitedto oxidation or other reactions as well as spin, thermal, or acoustictransportation).

While the exemplary preferred embodiments of the present invention aredescribed herein with particularity, those skilled in the art willappreciate various changes, additions, and applications other than thosespecifically mentioned, which are within the spirit of this invention.

1. The method of determining spatially-resolved material properties froma sample's complex reflectance or transmittance comprising the steps of:a. providing at least partially spatially-coherent radiation in the formof an incident beam; b. characterizing the incident beam; c. deliveringthe incident beam onto a sample to produce scattered radiation; d.varying at least one independent parameter of the incident beam uponwhich the sample's complex reflectance or transmittance is dependent; e.collecting the scattered radiation at multiple values of the independentparameter on a detector and generating scatter data; f. generating atleast one spatially-resolved, complex image of the sample based upon thebeam characterization and the collected scatter data, at each of themultiple values of the independent parameter, without constraining theimages based on a structural model of the sample; g. calculatingspatially-resolved complex scattering properties of the sample based onthe images; and h. determining spatially-resolved, depth-dependentmaterial properties of the sample from the spatially-resolved complexscattering properties.
 2. The method of claim 1 wherein step 1h furtherincludes the steps of: guessing at least one sample model in whichspatially-resolved material properties are assigned a depth; estimatingpredicted reflectance/transmittance versus the independent parameterbased on the sample model; comparing the predictedreflectance/transmittance versus the independent parameter to acalculated measurement of reflectance/transmittance versus theindependent parameter; and refining the sample model until the predictedreflectance/transmittance versus the independent parameter substantiallyagrees with the measured reflectance/transmittance versus theindependent parameter.
 3. The method of claim 2 wherein the step ofrefining the sample model uses a genetic algorithm.
 4. The method ofclaim 1 wherein step 1h uses either the amplitude or phase of thecomplex scattering properties.
 5. The method of claim 1, wherein step 1hassigns at least one of the following to the spatially-varying depthprofile: dopant density; material density; material composition; layerthickness; surface roughness; or interfacial mixing (diffusion) ofinterfaces between layers.
 6. The method of claim 1 wherein step 1aprovides vacuum ultraviolet (VUV) or deep UV or shorter wavelengthlight.
 7. The method of claim 6, further including the step ofgenerating the light via high harmonic generation.
 8. The method ofclaim 1 wherein step 1a includes one of the following steps: providingmultiple illuminating wavelengths simultaneously incident on the sample;providing multiple illuminating wavelengths in sequence incident on thesample; providing multiple polarization states of the incident beam;providing multiple spatial modes of the incident beam; and wherein anindependent parameter in step 1d includes one of the following:radiation wavelength; relative incidence angle between the beam and thesample; radiation polarization; shape of the incident beam.
 9. Themethod of claim 1 further comprising the step of moving the samplerelative to the incident beam and collecting the scattered radiation formultiple values of the independent parameter.
 10. The method of claim 1further comprising the step of moving the camera with respect to thescattered radiation to extend the resolution of the imaging systembetween variations of the independent parameter.
 11. The method of claim1 wherein step 1b includes the step of measuring beam power.
 12. Themethod of claim 11 further including the step of repeatedly measuringthe beam power during step 1e.
 13. The method of claim 11 furthercomprising the step of removing the sample from the incident beam pathwhile measuring beam power.
 14. The method of claim 1 wherein step 1bincludes the step of scattering the incident beam from a portion of thesample having known properties.
 15. The method of claim 1 wherein step1f further includes the step of using a ptychographic reconstructionalgorithm.
 16. Apparatus for measuring spatially-resolved materialproperties of a sample comprising: an optic that focuses an incidentbeam of light composed of wavelengths at or below the vacuum ultravioletonto the sample; a detector configured to collect light that scattersfrom the sample and generate scatter data; a device configured tomeasure power of the incident beam; and a processor configured toconvert scatter data and measured power of the incident beam intospatially-resolved, complex images of the sample, and determinespatially-resolved material properties of the sample from thespatially-resolved complex images.
 17. The apparatus of claim 16 whereinthe device includes an optic to divert a portion of the beam to thedetector.
 18. The apparatus of claim 16 further comprising at least oneof the following: a mechanism configured to rotate the sample relativeto the incident beam; a mechanism configured to translate the samplerelative to the incident beam; a mechanism configured to rotate thedetector relative to the sample; a mechanism for selectively removingthe sample from a path of the beam between the optic and the detector;19. The apparatus of claim 16 further including a mechanism to alter thewavelength of the radiation on the sample.